Barack Obama has ratcheted up the pressure on Pakistan, demanding that the Pakistani government investigate whether its own people were involved in a network to support Osama bin Laden in his Abbottabad hideout.

The US president's comments are his most direct yet on the subject of Pakistan's possible complicity with terrorism. He told the CBS show 60 Minutes that Bin Laden must have had "some sort of support network" inside the country.

"We don't know whether there might have been some people inside of government, outside of government, and that's something we have to investigate, and more importantly, the Pakistani government has to investigate," he said. The president also told the programme he didn't lose sleep over the possibility that Bin Laden might be killed. Anyone who questions whether the terrorist mastermind didn't deserve his fate "needs to have their head examined," he said.

Obama's words add to a sustained verbal attack by the US administration on the Pakistani government in the wake of the raid on the al-Qaida leader's lair in the middle of a busy garrison town that is home to three regiments, a military academy and thousands of soldiers.

Last week the CIA director, Leon Panetta, told Congress that Pakistan had been "either involved or incompetent".Tom Donilon, the national security adviser, said on ABC's This Week that there was no evidence that Pakistan had knowledge of Bin Laden's presence.

But he said the al-Qaida chief "was living, and we now know operating, in a town 35 miles away from Islamabad, a military town. So questions are being raised quite aggressively in Pakistan". Donilon said the US would remain "cool and calm". But he added: "They need to do an investigation."

Donilon also said that the US was urging Pakistan to give it access to Bin Laden's three widows. Information from the women, who remained in the house after the commandos killed Bin Laden, might answer questions about whether Pakistan harboured the al-Qaida chief as many American officials are speculating. It could also reveal details about Bin Laden's day-to-day life, his actions since the invasion of Afghanistan in 2001, and the inner workings of al-Qaida.

The women, along with several children picked up from the house, are believed to be in Pakistani army custody.

One objective of the intensifying pressure on Pakistan is to ensure its co-operation with the CIA and other US investigators into the treasure trove of documents found inside Bin Laden's compound. Most of the materials – amounting to the single largest cache of information taken from a senior terrorist, equivalent in size to a small college library, officials say – were taken away by the US Navy Seals and are being pored over by federal anti-terrorism investigators.

But a substantial number of documents were left behind and are now held by Pakistani officials, who are also holding in custody the non-combatants found in the compound, including Bin Laden's three wives and several children. The US wants to be able to question the wives.

The pressure from Washington puts the Pakistani government in an awkward position. The fact that Bin Laden was holed up for so long in the middle of the country is a huge embarrassment, but so too is the unannounced US raid inside its sovereign territory.

That conflict is reflected in the position of the army chief, General Ashfaq Kayani, who has announced that he is leading an investigation into what happened. He has warned the US not to try another stealth mission inside the country.

Pakistan's ambassador to Washington, Hussain Haqqani, promised "heads would roll" once Kayani's investigation was completed. "If someone is complicit, there will be zero tolerance for that," he told This Week. "If any member of the Pakistan government, military or intelligence service knew were Osama bin Laden was we would have taken action. Osama bin Laden's presence in Pakistan was not to Pakistan's advantage."

Pakistan's prime minister, Yousaf Raza Gilani, is due to make a statement to parliament, his first formal comments on the Bin Laden issue. Opposition figures have called for his resignation over the affair.

Until now most western criticism has been directed at Pakistan's military and intelligence agencies. Some US officials have insinuated that the powerful Inter-Services Intelligence helped harbour Bin Laden. The ISI is hitting back with media leaks. In a move bound to infuriate the US, several Pakistani television stations on Friday named the CIA station chief in Islamabad as Mark Carlton. The stations said he had been given a verbal roasting by the ISI chief, General Shuja Pasha.

The naming is sensitive because the previous CIA chief in Islamabad quit his position over security worries last December after being named in a court case and the national media. But a senior Pakistani official insisted the named figure was not the station chief.

"There's no Mark Carlton. Someone must have heard a similar-sounding name and leaked it," he said.

The Pakistani government has introduced curbs on international media in Abbottabad, ordering television stations to cease broadcasting and some reporters to leave town.

On Saturday night the television regulator, Pemra, ordered nine international channels – including the BBC, CNN and Fox – to stop "illegal" broadcasts.

It suggested the channels could not broadcast from Abbottabad or anywhere in Pakistan without obtaining a licence, a previously unstated requirement.

Officials contacted several British, Australian and American journalists and instructed them to leave Abbottabad because their visas did not permit them to stay.

The government also took measures to stop more journalists entering Pakistan. At diplomatic missions in London and New Delhi, Pakistani officials said there was a temporary hold on media visas.

The measures appear to be part of a concerted government effort to stem a tide of critical media coverage over Bin Laden.